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<h1 class="reftitle">separate</h1>
<h2>Purpose</h2>
<p>Computes separating hyperplane between the set and given point.</p>
<h2>Syntax</h2>
<pre class="synopsis">h = separate(S,x)</pre>
<pre class="synopsis">h = S.separate(x)</pre>
<h2>Description</h2>
<p></p>
        Compute a separating hyperplane between the convex <tt>Set</tt> and the given point <tt>x</tt>.
        If <tt>Set</tt> is an array, the hyperplanes are returned as a cell array.
	<h2>Input Arguments</h2>
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<td><tt>S</tt></td>
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<p></p>Any set derived from <tt>ConvexSet</tt> class, e.g. <tt>YSet</tt> or <tt>Polyhedron</tt>.<p>
	    		Class: <tt>ConvexSet</tt></p>
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<td><tt>x</tt></td>
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<p></p>The point given as vector in the same dimension as <tt>ConvexSet</tt>.<p>
	    		Class: <tt>double</tt></p>
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<h2>Output Arguments</h2>
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<td><tt>h</tt></td>
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<p></p>Separating hyperplane defined as <img src="../../../../../../fig/mpt/modules/geometry/sets/@ConvexSet/separate1.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@ConvexSet/separate1.png">.
      <p>
	    		Class: <tt>double</tt></p>
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<h2>Example(s)</h2>
<h3>Example 
				1</h3>Describe a convex using YALMIP<pre class="programlisting">x = sdpvar(2,1);</pre>
<pre class="programlisting"></pre>
<pre class="programlisting">F = set(0.3*x'*x -0.7*x(1)&lt;=1) + set(-x(1)+2.3*x(2)&lt;=0.5);</pre>
<pre class="programlisting"></pre>
<pre class="programlisting">S = YSet(x,F); </pre>
<pre class="programlisting"></pre> Compute the separating hyperplane from the point <tt>v=[-2,2]</tt> 
      <pre class="programlisting"> v = [-3;2]; </pre>
<pre class="programlisting"></pre>
<pre class="programlisting"> h = S.separate(v) </pre>
<pre class="programlisting">
h =

          2.01047891957449         -2.21283525231897         -5.98777459338193

</pre> Construct a new polyhedron out of the hyperplane and plot the sets <pre class="programlisting"> P = Polyhedron('He',h); </pre>
<pre class="programlisting"></pre>
<pre class="programlisting"> S.plot; hold on; axis([-4 4 -3 3]); text(v(1),v(2),'x'); P.plot; </pre>
<pre class="programlisting">Plotting...
28 of 40
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<p class="programlistingindent"><img src="../../../../../../fig/mpt/modules/geometry/sets/@ConvexSet/separate_img_1.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@ConvexSet/separate_img_1.png" width="60%"></p>
<h2>See Also</h2>
<a href="./distance.html">distance</a>, <a href="./support.html">support</a><p></p>
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<br><p>©  <b>2010-2013</b>     Colin Neil Jones: EPF Lausanne,    <a href="mailto:colin.jones@epfl.ch">colin.jones@epfl.ch</a></p>
<p>©  <b>2010-2013</b>     Martin Herceg: ETH Zurich,    <a href="mailto:herceg@control.ee.ethz.ch">herceg@control.ee.ethz.ch</a></p>
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